The Nehari manifold method for discrete fractional p-Laplacian equations

The Nehari Manifold for a Class of Elliptic Equations of P-laplacian Type

1 1 , , 0, , r s p u u h x u dx g x u dx x u x + + −∆ = + ∈ Ω = ∈ ∂Ω () 1, 0 p W Ω () () () 1 1 , 0. r s p u x h x u dx g x u dx in u on + +  −∆ = + Ω   = ∂Ω   () E () () 1 1 / r p s Np N p N p < < − < < − + − () () () 0 0 r h L L C ∞ ∈ Ω Ω Ω   0 1 1 1, r r p * + + = ()() 0. 1 Np r Np r N p = − + − () () 0 s g L L ∞ ∈ Ω Ω  0 1 1 1, s s p * + + = ()() 0 ,. 1 Np Np s p Np s N p N p *   ...

The Nehari Manifold for Fractional Systems Involving Critical Nonlinearities

We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at least two positive solutions when the pair of parameters (λ, μ) belongs to a suitable subset of R.

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Nonlocal discrete p-Laplacian Driven Image and Manifold Processing

A framework for non local discrete p-Laplacian regularization on Image and Manifold represented by weighted graphs of the arbitrary topologies is proposed. The proposed discrete framework unifies the local and non local regularization for image processing and extends them to the processing of any discrete data living on graphs. To cite this article: A. Elmoataz, O. Lezoray, S. Bougleux, C. R. M...

Existence of solutions for p-Laplacian discrete equations

This work is devoted to the study of the existence of at least one (non-zero) solution to a problem involving the discrete p-Laplacian. As a special case, we derive an existence theorem for a second-order discrete problem, depending on a positive real parameter a, whose prototype is given by Duðk 1Þ 1⁄4 af ðk;uðkÞÞ; 8k 2 Z1⁄21; T ; uð0Þ 1⁄4 uðT þ 1Þ 1⁄4 0: ( Our approach is based on variational...